Kristin is evaluating a capital budgeting project that should last for 4 years.

Question

Kristin is evaluating a capital budgeting project that should last for 4 years. The project requires $700000 of equipment. She is unsure what depreciation method to use in her analysis, straight-line or the 3-year MACRS accelerated method. Under straight-line depreciation, the cost of the equipment would be depreciated evenly over its 4-year life (ignore the half-year convention for the straight-line method). The applicable MACRS depreciation rates are 33%, 45%, 15%, and 7%. The company's WACC is 13%, and its tax rate is 40%.
What would the depreciation expense be each year under each method? Round your answers to the nearest cent.

Year Scenario 1
(Straight-Line) Scenario 2
(MACRS)
1 $ $
2 $ $
3 $ $
4
$

$
Which depreciation method would produce the higher NPV?


How much higher would the NPV be under the preferred method? Round your answer to two decimal places.
$

Explanation / Answer

a. Depreciation under straight line is $ 2,000,000 each year for 1st to 4th year.

Depreciation based on MACRS accelerated method is:
Depreciation rate x cost of project = depreciation charge

Depreciation Year 1 =8000000 x .33= 2640000
Depreciation Year 2= 8000000 x .45= 3600000
Depreciation Year 3= 8000000 x .15= 1200000
Depreciation Year 4 = 8000000 x .07= 560000

b. MACRS depreciation will produce a higher NPV by $ 127816

Present value of tax shield under straight line depreciation is

Depreciation x .4 ( tax rate) = Tax Shield x Present Value Factor of 1 at year n = present value

Year 1 cash in due to tax shield = 2000000 x .40= 800000 x 0.909090909= 727273
Year 2 cash in due to tax shield = 2000000 x .40= 800000 x 0.826446281= 661157
Year 3 cash in due to tax shield = 2000000 x .40= 800000 x 0.751314801= 601052
Year 4 cash in due to tax shield = 2000000 x .40= 800000 x 0.683013455= 546411
Total Present value of tax shield under straight line depreciation= 2535892
Year 0 cash out - 8,000,000 x 1. ( present value of $1 at year 0) = -8000,000
Net Present Value (straight line depreciation) ............ -5464108


Present value of tax shield of depreciation under MACRS:

Year 1 cash in due to tax shield = 2640000 x .40= 1056000 x 0.909090909= 960000
Year 2 cash in due to tax shield = 3600000 x .40= 1440000 x 0.826446281= 1190083
Year 3 cash in due to tax shield = 1200000 x .40= 480000 x 0.751314801= 360631
Year 4 cash in due to tax shield = 560000 x .40 = 224000 x 0.683013455= 152995
Total Present value of cash in due to tax shield under MACRS= 2663709
Year 0 cash out = -8000000 x 1.0 ( present value of 1 at year 0) = -8000000
NPV ( MACRS depreciation.) =-5336291

Difference in Net Present value between St line and MACRS depreciation is $ 127816
in favor of MACRS depreciation.
-5464108 minus -5336291= -127816

Depreciation is a tax deductible expense. With depreciation, you save on paying income tax.
So, the tax saving is a cash inflow.

If Depreciation is not tax deductible, then you would have to pay higher income tax.

Present value factor of $1 at 10%
Year 0 =1
Year 1 = 1/1.1= 0.909090909
Year 2 = 0.909090909 divided by 1.10 =0.826446281

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